Ultimate External Thread Tool — Major, Pitch and Minor Diameter Limits for UNC, UNF, UNEF, UN, UNR, UNS, UNJ, Metric M and MJ Bolts and Screws

Major, Pitch and Minor Diameters for Every External Thread

The companion to the Ultimate Internal Thread Tool: limits of size for bolts, screws and studs. It covers Unified inch threads (UNC, UNF, UNEF, constant-pitch UN and UNR) in Class 2A and 3A, UNS specials such as 1/4-40, UNJ aerospace threads with their root radius, and ISO metric M (6g, 4g6g, 6h) and MJ (4h6h) threads. Each row gives the allowance and the major, pitch and minor diameter limits.

Every value is computed from the formulas in ASME B1.1-2024, SAE AS8879B, ASME B1.13M and ASME B1.21M. Select any row, or its ⊞ box, for the profile drawing, every dimension, ring and snap gage sizes and the roll-thread blank. Type a measured major or pitch diameter to see which threads it fits, add any special thread, and print a color or black-and-white report. To check a pitch diameter with wires, use the Thread Wire Measurement calculator.

EXTERNAL THREAD TOOL
major Ø · pitch Ø · minor Ø · allowance
Measured
in
Special thread
Any diameter and pitch: limits come straight from the standard's formulas.
Reference Guide — External Threads
01

Major, Pitch and Minor Diameter of a Bolt

The major diameter d is the outside of the bolt, across the thread crests. The minor diameter is at the roots. The pitch diameter d₂ sits between them, where the ridge and the groove are equally wide. The pitch diameter decides the fit with the nut.

Each external class gives a maximum and a minimum for the major and pitch diameters. The maximum is the basic size less the allowance es, and the minimum is the maximum less the tolerance.

Limits of size, external thread (ASME B1.1 para 8.3.1)\[ \begin{aligned} d_{\max} &= D - es \qquad d_{\min} = d_{\max} - T_d \\ d_{2\,\max} &= D - 0.64951905P - es \\ d_{2\,\min} &= d_{2\,\max} - T_{d2} \end{aligned} \]
Tolerances and allowance (ASME B1.1 para 5.8.1)\[ \begin{aligned} T_{d2}(2A) &= 0.0015\sqrt[3]{D} + 0.0015\sqrt{LE} + 0.015\sqrt[3]{P^2} \\ T_{d2}(3A) &= 0.75\,T_{d2}(2A) \\ T_d &= 0.060\sqrt[3]{P^2} \quad (2A,\,3A) \\ es &= 0.300\,T_{d2}(2A) \;(2A), \quad 0 \;(3A) \end{aligned} \]

\(LE\) is the length of engagement: \(D\) for the coarse, fine, 4-, 6- and 8-UN series, 9 pitches for the others and for UNS specials. Enter a known length in a thread's window to recompute its pitch diameter tolerance. Every value on this page was checked against all 716 Class 2A and 3A rows of B1.1 Table 2A and the 114 UNS sizes of Table D-1.

02

UN, UNR and UNJ Roots

UN external threads may have a flat or rounded root. Their minor diameter is not specified: a GO thread gage controls it, and the values shown are references. UNR is the same thread with a mandatory rounded root of radius not less than 0.108P. Most rolled bolts are UNR. A UNR bolt mates with a UN nut.

Reference minor diameters (para 8.3.1(e), (f))\[ \begin{aligned} d_{1\,\max}^{UN} &= D - 1.08253175P - es \\ d_{3\,\max}^{UNR} &= D - 1.22686932P - es \\ d_{1\,\min} &= d_{2\,\min} - 0.64951905P \end{aligned} \]

UNJ external threads have a controlled root radius of 0.15011P to 0.18042P and a specified minor diameter. The fuller root lowers the stress concentration and raises fatigue life. Because the root is deeper into the radius, the mating internal UNJ thread has a raised minor diameter; see the Internal Thread Tool for its larger tap drill.

UNJ minor diameter (para 8.3.1(e)(3), AS8879B Table 9)\[ \begin{aligned} d_{3\,\max} &= d_{2\,\max} - 0.50518P \\ d_{3\,\min} &= d_{2\,\min} - 0.56580P \end{aligned} \]
03

Metric M and MJ: 6g, 4g6g, 6h and 4h6h

A metric external class names the pitch diameter grade, the position letter and the major diameter grade. g has an allowance (fundamental deviation) of about \(0.015 + 0.011P\) mm; h has none. 6g is the general-purpose bolt class, the metric counterpart of 2A. 4g6g is a closer fit, and 6h is used where there is no room for an allowance or the bolt is plated to size.

ASME B1.13M para 9.3.2\[ \begin{aligned} d_{\max} &= D - es, \quad d_{2\,\max} = D - 0.6495191P - es \\ d_{1\,\max} &= d_{2\,\max} - 0.4330127P \;\;(\text{flat root}) \\ d_{3\,\min} &= d_{2\,\min} - 0.6160254P \;\;(r \ge 0.125P) \end{aligned} \]

The tolerances \(T_d\) and \(T_{d2}\) are the B1.13M Table 11 and Table 12 values (ISO 965-1), by pitch and diameter range. Where a pitch is not tabulated for a range, the Section 6 formulas are used, rounded to R40, and the row is marked. Values were checked against B1.13M Table 15, for example M8×1.25-6g: pitch Ø 7.160 / 7.042, flat-root minor 6.619, rounded-root minor min 6.272.

MJ (ASME B1.21M) bolts are class 4h6h, with a 0.15011P to 0.18042P root radius and the same \(0.50518P\) and \(0.56580P\) minor diameter rules as UNJ.

04

Checking a Bolt: Gages, Wires and Blanks

A GO thread ring must screw on: it checks that the functional size (pitch diameter with lead and angle errors added) is no larger than d₂ max. A NOT GO (LO) ring must not go on by more than a few turns: it checks the pitch diameter is no smaller than d₂ min. Plain rings or snap gages check the major diameter.

Without ring gages, measure the pitch diameter with three wires and a micrometer. Each thread's window has a link to the Thread Wire Measurement calculator with the thread filled in.

Plated threads. The 2A and g allowance is the room for plating. After plating, the thread must still accept a GO gage at basic size (3A or h). Class 3A and h threads have no allowance and must be made undersize for plating.

Roll-thread blank (shop practice). The window shows the mean pitch diameter as an approximate blank diameter for rolled threads. The exact blank depends on the material, the root form and the dies. Use your die maker's figure and adjust after the first parts.
05

Pipe and Whitworth Threads

BSW, BSF and BSPP (G) use the 55° Whitworth form. Their limits are the American Truncated Whitworth tables of NBS Handbook H28 (1944), which mate fully with BS 84 threads. Medium is class 2 and Close is class 3. Neither has an allowance. The major diameter is truncated \(0.147835P\) below basic; a full-form BS 84 screw may be up to the basic major diameter.

NPT and NPTF are tapered 1:16 on diameter. Their rows show the basic sizes at the large end (max: E2, at the end of the effective thread L2) and the small end (min: E0), from H28 (1957) Table VII.2. These are positions along the taper, not tolerance limits: a taper thread is gauged by its stand-off in an L1 ring gauge, ±1 turn.

BSPT (R) is estimated. ISO 7-1 is not publicly available. The BSPT rows give the gauge-plane sizes of H28 Table 151 and estimate the small end with the NPT hand-tight length. They are marked unverified.
06

Sources

  • ASME B1.1-2024, Unified Inch Screw Threads (UN, UNR, and UNJ Thread Forms). Table 1, Table 5, paras 5.3, 5.8.1 and 8.3.1, Appendix D. Results checked against Tables 2A and D-1.
  • SAE AS8879B (2001), Screw Threads — UNJ Profile, Inch, Controlled Radius Root with Increased Minor Diameter. Table 9.
  • ASME B1.13M-1995, Metric Screw Threads: M Profile. Tables 3, 8, 11 and 12 and para 9.3.2 (ISO 965-1). Results checked against Table 15.
  • ISO 261:1998, ISO general purpose metric screw threads — General plan. Table 2.
  • ASME B1.21M-1978, Metric Screw Threads: MJ Profile. Para 6.8.1 and Table 3.
  • NBS Handbook H28 (1944), Screw-Thread Standards for Federal Services, Appendix 4, American Truncated Whitworth threads (ASA B1.6-1944), Tables 148 to 151: BSW, BSF and BSPP limits, fully interchangeable with BS 84-1940. Public domain: nvlpubs.nist.gov.
  • NBS Handbook H28 (1957) Part II, Screw-Thread Standards for Federal Services, Section VII, Table VII.2 (NPT basic dimensions), and Table VII.1 (thread form). Public domain: nvlpubs.nist.gov.
  • ISO 7-1 (BSPT) is not publicly available. BSPT rows use the H28 Table 151 pipe gauge diameters and an estimated small end, and are marked unverified.